On this animation, you can see a proton (in magenta) coming from the
right and an electron (in blue) coming from the left. The proton is made
up of three quarks (Green, red and blue) and as the phenomena that interests
us occurs at the quarks scale, we can see the proton just as a group of
quarks.
The electron hits one of these quarks. The three quarks are scattered
into a direction whereas the electron goes into an excited state for a
few instants. After it decays back into an electron and a photon (or into
other particles if an other decay mode was choosen).